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R. C. Robinson, “An Introduction to Dynamical Systems: Conti-nuous and Discrete,” Pearson Prentice Hall, New Jersey, 2004.

has been cited by the following article:

• TITLE: Investigation of the Mechanism of Tangent Bifurcation in Current Mode Controlled Boost Converter

  AUTHORS: Ling-ling Xie, Ren-xi Gong, Kuang Wang, Hao-ze Zhuo

  KEYWORDS: Tangent Bifurcation, Discrete Iterative Map, Boost Converter, Continuous Current Mode (CCM)

  JOURNAL NAME: Circuits and Systems, Vol.2 No.1, January 27, 2011

  ABSTRACT: Tangent bifurcation is a special bifurcation in nonlinear dynamic systems. The investigation of the mechanism of the tangent bifurcation in current mode controlled boost converters operating in continuous conduction mode (CCM) is performed. The one-dimensional discrete iterative map of the boost converter is derived. Based on the tangent bifurcation theorem, the conditions of producing the tangent bifurcation in CCM boost converters are deduced mathematically. The mechanism of the tangent bifurcation in CCM boost is exposed from the viewpoint of nonlinear dynamic systems. The tangent bifurcation in the boost converter is verified by numerical simulations such as discrete iterative maps, bifurcation map and Lyapunov exponent. The simulation results are in agreement with the theoretical analysis, thus validating the correctness of the theory.